code: def test_orthogonal_procrustes_exact_example():
      # Check a small application.
      # It uses translation, scaling, reflection, and rotation.
      #
      #         |
      #   a  b  |
      #         |
      #   d  c  |        w
      #         |
      # --------+--- x ----- z ---
      #         |
      #         |        y
      #         |
      #
      A_orig = np.array(
          [[-3, 3], [-2, 3], [-2, 2], [-3, 2]], dtype=float
      )
      B_orig = np.array([[3, 2], [1, 0], [3, -2], [5, 0]], dtype=float)
      A, A_mu = _centered(A_orig)
      B, B_mu = _centered(B_orig)
      R, s = orthogonal_procrustes(A, B)
      scale = s / np.square(norm(A))
      B_approx = scale * np.dot(A, R) + B_mu
      assert_allclose(B_approx, B_orig, atol=1e-8)
  
file_path: scipy/scipy/linalg/tests/test_procrustes.py
imports: from itertools import product, permutations
  import numpy
  from numpy.testing import assert_array_less, assert_allclose
  from pytest import raises
  from scipy.linalg import inv, eigh, norm
  from scipy.linalg import orthogonal_procrustes
  from scipy.sparse._sputils import matrix
label_desc: Use image node_id 9 for calling a global function with example usage: test_orthogonal_procrustes_exact_example() without return types